Common fixed points of commuting mappings

Authors:
William J. Gray and Carol M. Smith

Journal:
Proc. Amer. Math. Soc. **53** (1975), 223-226

MSC:
Primary 54H25

MathSciNet review:
0377843

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a dendroid and an abelian semigroup of continuous monotone self-mappings of . A point is fixed under if for all . Let be continuous and commute with each element of . It is shown that and have a common fixed point.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1975-0377843-1

Keywords:
Dendroid,
abelian semigroup,
monotone mapping,
open mapping,
arc order,
hereditarily unicoherent continuum

Article copyright:
© Copyright 1975
American Mathematical Society